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If x ≠ 0, what is the value of x ? (1) |x^x| = 1 (2) x^5 = x^x

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Math Expert
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Joined: 02 Sep 2009
Posts: 52344
If x ≠ 0, what is the value of x ? (1) |x^x| = 1 (2) x^5 = x^x  [#permalink]

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New post 20 May 2018, 13:22
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

51% (01:01) correct 49% (00:56) wrong based on 170 sessions

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Re: If x ≠ 0, what is the value of x ? (1) |x^x| = 1 (2) x^5 = x^x  [#permalink]

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New post 20 May 2018, 13:57
2
Bunuel wrote:

GMAT Club Tests Fresh Question:



If x ≠ 0, what is the value of x ?


(1) \(|x^x| = 1\)

(2) \(x^5 = x^x\)


We'll try finding numbers which give contradictory answers.
This is an Alternative approach.


(1) So x^x must equal 1 or -1. This can happen if the exponent is 0 which is impossible by question definition or if x = 1 or if x = -1.
That is, 1^1 = 1 and -1^-1 = -1 so in absolute value both equal 1.
Insufficient.

(2) If we're not sure where to start we'll try easy numbers. If x = 1 then 1^5 = 1^1 = 1 so x = 1 works. If x = 2 then 2^5 = 32 but 2^2 = 4 so x = 2 doesn't work. Since the exponent on the left is 5 it makes sense to try x = 5 which gives 5^5 = 5^5. So x = 1 and x = 5 both work.
Insufficient.

Combined:
x = 1 fits both criteria as shown above. How about x = -1? -1^5 = -1 and -1^-1 = -1. So both x = 1 and x = -1 fit both criteria.
Insufficient.

(E) is our answer.
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Re: If x ≠ 0, what is the value of x ? (1) |x^x| = 1 (2) x^5 = x^x  [#permalink]

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New post 20 May 2018, 14:03
1
My answer:E

St1: X=1 or x=-1
St2: x=1 or x=-1


Sent from my iPhone using GMAT Club Forum mobile app
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Re: If x ≠ 0, what is the value of x ? (1) |x^x| = 1 (2) x^5 = x^x  [#permalink]

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New post 24 Dec 2018, 03:10
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Re: If x ≠ 0, what is the value of x ? (1) |x^x| = 1 (2) x^5 = x^x  [#permalink]

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New post 03 Jan 2019, 10:25
Bunuel wrote:

GMAT Club Tests' Fresh Question:



If x ≠ 0, what is the value of x ?


(1) \(|x^x| = 1\)

(2) \(x^5 = x^x\)



Hi Bunuel Sir.... Can you let me what is the mistake in my method .
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Re: If x ≠ 0, what is the value of x ? (1) |x^x| = 1 (2) x^5 = x^x &nbs [#permalink] 03 Jan 2019, 10:25
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